Mathematics
Substraction and addition of fractions
The addition and subtraction of fractions involve combining or taking away parts of a whole. When adding or subtracting fractions, it is important to have a common denominator. To add or subtract fractions with different denominators, the fractions must first be converted to equivalent fractions with a common denominator before performing the operation.
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12 Key excerpts on "Substraction and addition of fractions"
eBook - PDF- Charles P. McKeague(Author)
- 2011(Publication Date)
- XYZ Textbooks(Publisher)
190 Chapter 3 Fractions 2: Addition and Subtraction As a summary of what we have done so far, and as a guide to working other problems, we now list the steps involved in adding and subtracting fractions with different denominators. The idea behind adding or subtracting fractions is really very straight-forward. We can only add or subtract fractions that have the same denominators. If the fractions we are trying to add or subtract do not have the same denominators, we rewrite each of them as an equivalent fraction with the LCD for a denominator. Here are some additional examples of sums and differences of fractions. EXAMPLE 7 Subtract 3 } 5 2 1 } 6 . SOLUTION The LCD for 5 and 6 is their product, 30. We begin by rewriting each fraction with this common denominator: 3 } 5 2 1 } 6 5 3 ⋅ 6 } 5 ⋅ 6 2 1 ⋅ 5 } 6 ⋅ 5 5 18 } 30 2 5 } 30 5 13 } 30 EXAMPLE 8 Add 1 } 6 1 1 } 8 1 1 } 4 . SOLUTION We begin by factoring the denominators completely and building the LCD from the factors that result: 8 divides the LCD 6 5 2 ? 3 8 5 2 ? 2 ? 2 4 5 2 ? 2 6 LCD 5 2 ? 2 ? 2 ? 3 5 24 4 divides the LCD 6 divides the LCD We then change to equivalent fractions and add as usual: 1 } 6 1 1 } 8 1 1 } 4 5 1 ⋅ 4 } 6 ⋅ 4 1 1 ⋅ 3 } 8 ⋅ 3 1 1 ⋅ 6 } 4 ⋅ 6 5 4 } 24 1 3 } 24 1 6 } 24 5 13 } 24 To Add or Subtract Any Two Fractions Step 1 Factor each denominator completely, and use the factors to build the LCD. (Remember, the LCD is the smallest number divisible by each of the denominators in the problem.) Step 2 Rewrite each fraction as an equivalent fraction with the LCD. This is done by multiplying both the numerator and the denominator of the frac- tion in question by the appropriate whole number. Step 3 Add or subtract the numerators of the fractions produced in Step 2. This is the numerator of the sum or difference. The denominator of the sum or difference is the LCD. Step 4 Reduce the fraction produced in Step 3 to lowest terms if it is not al- ready in lowest terms. m8 m8 m m888 m888888 m88 m88888
eBook - ePubA Focus on Fractions
Bringing Mathematics Education Research to the Classroom
- Marjorie M. Petit, Robert E. Laird, Caroline B. Ebby, Edwin L. Marsden(Authors)
- 2022(Publication Date)
- Routledge(Publisher)
11Addition and Subtraction of FractionsDOI: 10.4324/9781003185475-11Big Ideas- Procedural fluency and conceptual understanding work together to deepen student understanding of fraction addition and subtraction.
- Conceptual understanding of addition and subtraction of fractions is built using visual models, estimation, unit fraction understanding, equivalence, and properties of operations.
Conceptual Understanding and Procedural Fluency
An important goal of fraction instruction is to ensure that students develop procedural fluency when adding and subtracting fractions. “Procedural fluency refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently” (National Research Council [NRC], 2001, p. 121).It is important to understand, however, that procedural fluency alone is not sufficient to ensure proficiency with addition and subtraction of fractions. Procedural fluency works together with conceptual understanding, each contributing to a deeper understanding of the other.Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which it is useful.(NRC, 2001, p. 118)Figure 11.1 shows Kenny’s strategy for solving a multistep fraction operation problem. Kenny finds and uses common denominators to add, then uses his understanding that2 3+1 4to find the missing fractional part.12 12= 1Kenny’s response. The response shows an understanding of equivalent fractions.Figure11.1To determine Kenny’s overall proficiency regarding adding and subtracting fractions, however, one would need to consider Kenny’s understanding of addition and subtraction across contexts and with a variety of fractions (e.g., fractions with the same and different denominators, mixed numbers). That said, the evidence suggests that Kenny is on his way to becoming both procedurally fluent and conceptually sound with fraction addition and subtraction.
eBook - PDF- Robert Reys, Mary Lindquist, Diana V. Lambdin, Nancy L. Smith, Anna Rogers, Audrey Cooke, Bronwyn Ewing, Kylie Robson(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Once again 5 12 , which is just under one-half, compares well with 42% and is the best choice. The conceptual understanding needed for fraction addition and subtraction is also important when determining the reasonableness of answers using digital technologies. CHAPTER 12 Fractions and decimals: meanings and operations 419 Addition and subtraction To help with building understanding of addition and subtraction of fractions, it is recommended not to start with a symbolic sentence such as 2 3 + 1 4 , but to begin with real-world problems that involve combining and separating. Such problems, together with concrete and pictorial models and using language that is meaningful, can help children: • see that adding and subtracting fractions might be similar to solving problems involving whole numbers • develop an idea of the reasonableness of an answer • see why a common denominator is needed when adding or subtracting fractions with related or unlike denominators. Building on children’s prior knowledge of fraction meaning and models will be beneficial when solving addition and subtraction problems involving fractions. Looking at the word problems in figure 12.6, children with a strong foundation in fractions should be able to solve problem B, knowing that like fractions can be added. There is a similarity with problem A: adding Georgia’s two kilometres to Ammar’s one kilometre, is like adding Georgia’s two-fifths of the swim circuit to Ammar’s one-fifth. Supporting the learners by asking them to draw a picture to illustrate their thinking will help them try problem C. Encourage children to discuss the similarities and differences presented in problem C compared to the other two problems. Again, a pictorial representation such as a rectangle might help. FIGURE 12.6 Three joining problems A Georgia ran two kilometres for the school fundraiser and Ammar ran one kilometre.
eBook - ePubThe Problem with Math Is English
A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics
- Concepcion Molina(Author)
- 2012(Publication Date)
- Jossey-Bass(Publisher)
Chapter Eight Operations with FractionsThe misconceptions and assumptions that permeate fractions only multiply when computation comes into play. As in other areas, methods for teaching the operations of fractions typically rely on shallow rules and procedures. The old adage “Ours is not to reason why; just invert and multiply” is yet another example of students learning a process without any idea of the conceptual basis for it. At the same time, the procedures for computing fractions and the results they produce can seem foreign to students used to working with whole numbers. Mystified and lost, students can feel like strangers in a strange land. To help students adjust to operations with fractions, teachers need to provide both a conceptual foundation that connects to whole number operations and guidance in interpreting the language and symbolism.Adding and Subtracting Fractions
Most teachers and students would probably consider addition and subtraction to be the easiest of the four basic operations. It is somewhat of a paradox then that many students find adding and subtracting fractions to be extremely challenging. Sometimes, though, what we know gets in the way of learning something new. The habits instilled in students when they add and subtract whole numbers, coupled with an inattention to the language and symbolism of math in instruction, can interfere with students' ability to learn the same two operations with fractions.So What's the Problem?
Examine Box 8.1, which illustrates a common error students make when adding fractions with unlike denominators. No doubt, countless teachers have been frustrated by trying to help students avoid this mistake.Box 8.1: Incorrect Addition of FractionsThe primary culprit behind this error is the lack of instructional emphasis on the property that only like items can be combined. Students are taught they can only add and subtract fractions with common denominators, but not why. By connecting to the role of like items in combining fractions, teachers can help students build on the conceptual foundation of whole-number addition and subtraction. Chapter Five, in the discussion on the order of operations, explains how math instruction initially emphasizes the property of like items in basic addition and subtraction. Students receive problems such as 2 apples + 3 apples = 5 apples, while also being told they can't add 2 apples to 3 oranges without converting to a common unit, such as fruit
eBook - PDF- Charles P. McKeague(Author)
- 2015(Publication Date)
- XYZ Textbooks(Publisher)
The idea behind adding or subtracting fractions is really very straight-forward. We can only add or subtract fractions that have the same denominators. If the fractions we are trying to add or subtract do not have the same denominators, we rewrite each of them as an equivalent fraction with the LCD for a denominator. Here are some additional examples of sums and differences of fractions. Subtract: 3 __ 5 − 1 __ 6 . Solution The LCD for 5 and 6 is their product, 30. We begin by rewriting each fraction with this common denominator: 3 __ 5 − 1 __ 6 = 3 ⋅ 6 ____ 5 ⋅ 6 − 1 ⋅ 5 ____ 6 ⋅ 5 = 18 ___ 30 − 5 ___ 30 = 13 ___ 30 Add: 1 __ 6 + 1 __ 8 + 1 __ 4 . Solution We begin by factoring the denominators completely and building the LCD from the factors that result: 8 divides the LCD 6 = 2 ⋅ 3 8 = 2 ⋅ 2 ⋅ 2 4 = 2 ⋅ 2 LCD = 2 ⋅ 2 ⋅ 2 ⋅ 3 = 24 4 divides the LCD 6 divides the LCD We then change to equivalent fractions and add as usual: 1 __ 6 + 1 __ 8 + 1 __ 4 = 1 ⋅ 4 ____ 6 ⋅ 4 + 1 ⋅ 3 ____ 8 ⋅ 3 + 1 ⋅ 6 ____ 4 ⋅ 6 = 4 ___ 24 + 3 ___ 24 + 6 ___ 24 = 13 ___ 24 To Add or Subtract Any Two Fractions Step 1 Factor each denominator completely, and use the factors to build the LCD. (Remember, the LCD is the smallest number divisible by each of the denominators in the problem.) Step 2 Rewrite each fraction as an equivalent fraction with the LCD. This is done by multiplying both the numerator and the denominator of the fraction in question by the appropriate whole number. Step 3 Add or subtract the numerators of the fractions produced in Step 2. This is the numerator of the sum or difference. The denominator of the sum or difference is the LCD. Step 4 Reduce the fraction produced in Step 3 to lowest terms if it is not already in lowest terms. Example 5 Example 6 158 Chapter 3 Fractions II: Addition and Subtraction Subtract: 3 − 5 __ 6 . Solution The denominators are 1 because 3 = 3 _ 1 and 6.
eBook - PDFMathematics for Elementary Teachers
A Contemporary Approach
- Gary L. Musser, Blake E. Peterson, William F. Burger(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
Some students initially view the addition of fractions as add- ing the numerators and adding the denominators as follows: 3 4 1 4 6 2 + = . Using this example, discuss why such a method for addition is unreasonable. Figure 6.18 illustrates how to add fractions when the denominators are not the same. Similarly, to find the sum 2 7 3 5 + , use the equality of fractions to express the fractions with common denominators as follows: 2 7 3 5 2 5 7 5 3 7 5 7 10 35 21 35 31 35 + = + = + = ¥ ¥ ¥ ¥ . This procedure can be generalized as follows. Figure 6.18 PROOF a b c d ad bd bc bd ad bc bd + = + = + Equality of fractions Addition with common denominators ■ Addition of Fractions with Unlike Denominators Let a b and c d be any fractions. Then a b c d ad bc bd + = + . T H E O R E M 6 . 4 Common Core – Grade 5 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (In general, a b c d ad bc bd / / / + = + ( ) .) Fourth graders know what addition means and know how to represent fractions in several different ways. Thinking like a fourth grader use pictures and words to find the following sum: 1 4 2 3 + . NOTE: Since you are thinking like a fourth grader, you may not know the usual procedure. If you use a common denomi- nator, you must explain why and how. Section 6.2 Fractions: Addition and Subtraction 225 In words, to add fractions with unlike denominators, find equivalent fractions with common denominators. Then the sum will be represented by the sum of the numera- tors over the common denominator. Reflection from Research The most common error when adding two fractions is to add the denominators as well as the numerators; for example, 1 2 1 4 + becomes 2 6 (Bana, Farrell, & McIntosh, 1995). Find the following sums and simplify. a. 3 7 2 7 + b.
eBook - PDFMathematical Practices, Mathematics for Teachers
Activities, Models, and Real-Life Examples
- Ron Larson, Robyn Silbey(Authors)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
Solve the problem. Write your answer as a proper fraction or mixed number in simplest form. a. - b. + 22. Addition and Subtraction Models Write the addition or subtraction problem represented by each model. Solve the problem. Write your answer as a proper fraction or mixed number in simplest form. a. - b. + 23. Adding and Subtracting with Unlike Denominators Find each sum or difference. Write your answer as a proper fraction or mixed number in simplest form. a. 3 — 4 − 5 — 12 b. 5 — 6 + 1 — 2 c. 6 — 7 + 3 — 14 d. 1 — 2 − 3 — 10 24. Adding and Subtracting with Unlike Denominators Find each sum or difference. Write your answer as a proper fraction or mixed number in simplest form. a. 4 — 5 + 1 — 10 b. 7 — 6 − 1 — 3 c. 5 — 4 + 1 — 6 d. 3 — 8 − 1 — 4 25. Adding or Subtracting Mixed Numbers Find each sum or difference. Write your answer in simplest form. a. 1 1 — 2 − 1 1 — 3 b. 2 3 — 4 − 1 1 — 8 c. 1 — 5 + 1 1 — 10 26. Adding or Subtracting Mixed Numbers Find each sum or difference. Write your answer in simplest form. a. 4 1 — 2 + 2 1 — 5 b. 3 1 — 2 − 1 1 — 6 c. 4 3 — 10 − 3 3 — 5 27. Using Fraction Strips Use fraction strips to find each difference. Write your answer in simplest form. a. 15 — 16 − 7 — 8 b. 2 — 5 − 2 — 15 c. 7 — 9 − 2 — 3 d. 4 — 5 − 3 — 10 28. Using Fraction Strips Use fraction strips to find each difference. Write your answer in simplest form. a. 5 — 12 − 1 — 3 b. 3 — 4 − 3 — 8 c. 7 — 12 − 1 — 6 d. 2 — 3 − 4 — 9 29. Estimation Use fraction strips to estimate each sum or difference. Then, find the exact answer. a. 11 — 12 − 3 — 4 b. 3 — 5 + 11 — 20 c. 1 — 2 − 5 — 13 30. Estimation Use fraction strips to estimate each sum or difference. Then, find the exact answer. a. 15 — 16 − 3 — 4 b. 3 — 7 + 3 — 10 c. 3 — 5 − 51 — 100 Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
eBook - PDF- Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis(Authors)
- 2020(Publication Date)
- Openstax(Publisher)
Step 2. Subtract the numerators. Step 3. Write the answer as a mixed number, simplifying the fraction part, if possible. 374 Chapter 4 Fractions This OpenStax book is available for free at http://cnx.org/content/col30939/1.6 We write the answer as a mixed number because we were given mixed numbers in the problem. TRY IT : : 4.183 Add: 1 5 6 + 4 3 4 . TRY IT : : 4.184 Add: 3 4 5 + 8 1 2 . EXAMPLE 4.93 Subtract: 4 3 4 − 2 7 8 . Solution Since the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD 8. Once in that form, we will subtract. But we will need to borrow 1 first. We were given mixed numbers, so we leave the answer as a mixed number. TRY IT : : 4.185 Find the difference: 8 1 2 − 3 4 5 . TRY IT : : 4.186 Find the difference: 4 3 4 − 1 5 6 . EXAMPLE 4.94 Subtract: 3 5 11 − 4 3 4 . Chapter 4 Fractions 375 Solution We can see the answer will be negative since we are subtracting 4 from 3. Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers. 3 5 11 − 4 3 4 Change to equivalent fractions with the LCD. 3 5 · 4 11 · 4 − 4 3 · 11 4 · 11 3 20 44 − 4 33 44 Rewrite as improper fractions. 152 44 − 209 44 Subtract. − 57 44 Rewrite as a mixed number. −1 13 44 TRY IT : : 4.187 Subtract: 1 3 4 − 6 7 8 . TRY IT : : 4.188 Subtract: 10 3 7 − 22 4 9 . MEDIA : : ACCESS ADDITIONAL ONLINE RESOURCES • Adding Mixed Numbers (http://www.openstax.org/l/24AddMixed) • Subtracting Mixed Numbers (http://www.openstax.org/l/24SubtractMixed) 376 Chapter 4 Fractions This OpenStax book is available for free at http://cnx.org/content/col30939/1.6 Practice Makes Perfect Model Addition of Mixed Numbers In the following exercises, use a model to find the sum. Draw a picture to illustrate your model. 436. 1 1 5 + 3 1 5 437. 2 1 3 + 1 1 3 438. 1 3 8 + 1 7 8 439. 1 5 6 + 1 5 6 Add Mixed Numbers with a Common Denominator In the following exercises, add.
- Catherine Sophian(Author)
- 2017(Publication Date)
- Routledge(Publisher)
Thus, for example, within the part–whole subconstruct, the denominator represents the number of parts into which the original unit is partitioned, and the numerator represents the number of those parts corresponding to the quantity being represented. The magnitude of the fraction decreases as the denominator gets larger, because the size of each part is decreasing, and the size increases as the numerator gets larger because more parts of that size are being included. Within the quotient interpretation, similarly, the numerator represents the dividend and the denominator the divisor of a division operation. The quotient decreases as the divisor increases and increases as the numerator decreases. The operator interpretation directly represents these inverse effects of numerator and denominator in terms of extending or stretching, on one hand, and contracting or shrinking, on the other.Thompson and Saldanha’s (2003) characterization of fractions in terms of the conception of two quantities as being in a “reciprocal relation of relative size” likewise underscores the conceptual coherence of fraction subconstructs. Their perspective, like the one advanced here, begins with the notion that fractions are fundamentally representations of magnitude. In addition, in recognizing that in order for one amount to be1 nthe size of another, the latter amount must be n times the size of the former, they emphasize the close link between fraction knowledge and multiplicative reasoning about many-to-one relations.THE INFORMATION-PROCESSING DEMANDS OF FRACTIONS
A number of accounts of fraction learning have called attention to the complexity of the information processing entailed in reasoning about fractions. Ohlsson (1991), for instance, argued that the concept of equivalent fractions is central to fraction arithmetic, and that it in turn entails a “schema of constancy under multiplicative compensation” (p. 39), that is, an appreciation of the fact that the inequality between the numerators of two equivalent fractions is offset by a proportionally equivalent inequality in the denominators. Kamii and Clark (1995) also emphasize the importance of multiplicative thinking in understanding fractions, but for them multiplicative thinking is closely related to the idea of one-to-many correspondence. It entails a hierarchical cognitive structure such that each individual item at one level corresponds to a group of items at the next lower level. Thus, for example, understanding the equivalence between1 4and3 12
eBook - PDF- Michael A. Calter, Paul A. Calter, Paul Wraight, Sarah White(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
To be able to separate a fraction into its partial fractions is important in calculus. We mention them here but will not calculate any until later. ◆◆◆ ◆◆◆ Exercise 3 ◆ Addition and Subtraction of Fractions Common Fractions and Mixed Numbers Combine and simplify. 1. 3 5 2 5 + 2. 1 8 3 8 - 3. 2 7 5 7 6 7 + - 4. 5 9 7 9 1 9 + - 5. 1 3 7 3 11 3 - + 6. 1 5 9 5 12 5 2 5 - + - 7. 1 2 2 3 + 8. 3 5 1 3 - 9. 3 4 7 16 + 10. 2 3 3 7 + 11. 5 9 1 3 3 18 - + 12. 1 2 1 3 1 5 + + Don’t use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. Rewrite each mixed number as an improper fraction. 13. 2 2 3 14. 1 5 8 15. 3 1 4 16. 2 7 8 17. 5 11 16 18. 9 3 4 Algebraic Fractions Combine and simplify. 19. a a 1 5 + 20. x x x 3 2 1 + - 21. a y a y 2 3 7 + - 22. x a y a z a 3 3 3 - + 23. x x 5 2 3 2 - 24. x x 7 2 5 2 + - + 25. x a b x b a 3 2 - + - 26. a x b x c x 2 2 2 - + 27. a a a 7 1 9 1 3 1 + + + - - - 28. a x x a x x a x x 2 ( 1) 3 2 2 - - - + - 29. a x a x 3 2 2 5 + 30. x y z 1 1 1 + + Mixed Form Rewrite each mixed expression as an improper fraction. 31. x x 1 + 32. x 1 2 - 33. x x x 1 1 1 1 - - - + 34. a a b 1 2 2 + - 35. a a 3 2 - - 36. x x x 5 2 3 2 - + 37. b x b b ax 3 1 2 + - - 38. x x x x 5 2 3 2 2 3 4 + + - - - 201 Section 9–4 ◆ Complex Fractions Applications Treat the given numbers in these problems as exact, and leave your answers in fractional form. 39. A certain work crew can grade 7 km of roadbed in 3 days, and another crew can do 9 km in 4 days. How much can both crews together grade in 1 day? 40. Liquid is running into a tank from a pipe that can fill the tank four times in 3 days. Meanwhile, liquid is running out from a drain that can empty two tankfulls in 4 days. What will be the net change in volume in 1 day? 41. A planer makes a 1 m cutting stroke at a rate of 15 m/min and returns at 75 m/min.
No longer available |Learn more- Tom Bassarear, Meg Moss(Authors)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
A quick estimation of the leading two digits shows 3100 1 2900 5 6000, so the answer is not true. Explorations Manual 3.7 Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Unless otherwise noted, all content on this page is © Cengage Learning Section 3.2 Understanding Subtraction 111 We have now examined addition and subtraction rather carefully. In what ways do you see similarities between the two operations? In what ways do you see differences? Think and then read on . . . . One way in which the two processes are alike is illustrated with the part–whole dia-gram used to describe each operation. These representations help us to see connections between addition and subtraction. In one sense, addition consists of adding two parts to make a whole. In one sense, subtraction consists of having a whole and a part and needing to find the value of the other part. We see another similarity between the two operations when we watch children de-velop methods for subtraction; it involves the “missing addend” concept. That is, the problem c 2 a can be seen as a 1 ? 5 c . We saw a related similarity in children’s strategies. Just as some children add large numbers by “adding up,” some children subtract larger numbers by “subtracting down.” Earlier in this section, subtraction was formally defined as c 2 b 5 a if a 1 b 5 c . The negative numbers strategy that some children invent brings us to an-other way of defining subtraction, which we will examine further in Chapter 4 when we examine negative numbers.
eBook - PDF- Alan Tussy, Diane Koenig(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
9 –– 15 5 –– 15 3 – 5 1 – 3 14 –– 15 + = We can use the following steps to add or subtract fractions with different denominators. 4.4 • Adding and Subtracting Fractions OBJECTIVE 2 Add and subtract fractions that have different denominators. Now we consider the problem 3 5 1 1 3 . Since the denominators are different, we cannot add these fractions in their present form. three-fifths 1 one-third Not similar objects To add (or subtract) fractions with different denominators, we express them as equivalent fractions that have a common denominator. The smallest common denominator, called the least or lowest common denominator, is usually the easiest common denominator to use. Least Common Denominator The least common denominator (LCD) for a set of fractions is the smallest number each denominator will divide exactly (divide with no remainder). Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. CHAPTER 4 • Fractions and Mixed Numbers 332 1 1 Add: 1 7 1 2 3 Strategy We will express each fraction as an equivalent fraction that has the LCD as its denominator. Then we will use the rule for adding fractions that have the same denominator. WHY To add (or subtract) fractions, the fractions must have like denominators. Solution Since the smallest number the denominators 7 and 3 divide exactly is 21, the LCD is 21. 1 7 1 2 3 5 1 7 ? 3 3 1 2 3 ? 7 7 To build 1 7 and 2 3 so that their denominators are 21, multiply each by a form of 1. 5 3 21 1 14 21 Multiply the numerators. Multiply the denominators.
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